Review on Application of Response Surface Method

J. Manuf. Sci. Prod., Vol. 12 (2012), pp. 17–24

Copyright © 2012 De Gruyter. DOI 10.1515/jmsp-2011-0010

Review on Application of Response Surface Method based Design of Experiments to Welding Processes

Kondapalli Siva Prasad,1; Chalamalasetti Srinivasa Rao2 and Damera Nageswara Rao3

analysis techniques such as ANOVA and regression analysis whereby the mathematical model shows the relationship between the input parameters and the output responses [2]. 1 Assistant Professor, Department of Mechanical EngiAmong the most prominently used DOE techniques are Reneering, Anil Neerukonda Institute of Technology & Sci- sponse Surface Methodology with Central Composite Deences, Visakhapatnam, India sign, Taguchi’s method and Factorial Design. In DOE, syn2 Associate Professor, Department of Mechanical Engiergy between mathematical and statistical techniques such neering, Andhra University, Visakhapatnam, India as Regression, Analysis of Variance (ANOVA), Non-Linear 3 Optimization and Desirability functions help to optimize Vice Chancellor, Centurion University, India the quality characteristics considered under a cost effective Abstract. Design of Experiment is one of the extensively process. ANOVA helps to identify the effect of each factor used method for experimental study of many manufactur- versus the objective function [3]. Experimental design was first introduced in 1920s by ing processes in engineering. In welding, Design of Experiments are widely used to develop a mathematical relation- R. A. Fischer who developed the basic principles of facship between the welding input parameters and the output torial design and the associated data analysis known as variables of the weld joint in order to determine the weld- ANOVA during research in improving the yield of agriculing input parameters that lead to the desired weld quality. tural crops [4]. In the present study, a review is made on Response Surface Method based Design of Experiments that have been em1.1 Factorial Method ployed for various welding processes by other researchers. This study predominantly focuses on the usage of Response Factorial design is used for conducting experiments as it alSurface Method in Welding. lows study of interactions between factors. Interactions are the driving force in many processes. Vital interface may Keywords. Design of experiment, mathematical model, be unobserved without factorial design of experiments. In response surface method, factorial method, welding. a full factorial experiment, responses are measured at all combinations of the experimental factor levels. The combiPACS® (2010). 81, 06. nations of factor levels represent the conditions at which responses are measured. Each experimental condition is called a “run” and the response measurement is called an “observation” while factorial design can be run on twolevels, three-levels and multi-level factorial. The entire set 1 Introduction of runs is the “design”. According to Myers and MontDesign of Experiment (DOE) is an experimental or analyti- gomery [5], Full Factorial Design is a design in which all cal method that is commonly used to statistically signify the possible combinations of the factor levels are fulfilled. The relationship between input parameters to output responses, result from the full factorial experiments would be more rewhere by a systematic way of planning of experiments, col- liable but conducting the full factorial experiments is costly lection and analysis of data is executed. DOE has wide ap- and sometimes prohibitive. plications especially in the field of science and engineering for the purpose of process optimization and development, process management and validation tests. A mathematical 1.2 Response Surface Method model has been developed by Avinash & Vinod [1] using Response Surface Method or commonly known as RSM is an anthology of statistical and mathematical methods that * Corresponding author: Kondapalli Siva Prasad, Department of Mechanical Engineering, Anil Neerukonda Institute of Technology & are helpful in generating improved methods and optimizing a welding process. RSM is more frequently used in Sciences, Sangivalasa, Bheemunipatnam Mandal, Visakhapatnam District, Andhra Pradesh, India, Pin Code: 531 162; analyzing the relationships and the influences of input paE-mail: [email protected]. rameters on the responses. The method was introduced by Received: October 31, 2011. Accepted: December 20, 2011. G. E. P. Box and K. B. Wilson in 1951. The main idea of

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K. Siva Prasad, Ch. Srinivasa Rao and D. Nageswara Rao

Figure 1. Circumscribed, inscribed and faced designs.

Design

Rotatable

Factor Levels

Yes Yes No

5 5 3

Circumscribed (CCC) Inscribed (CCI) Faced (CCF)

Uses Points Outside ˙1 Yes No No

Accuracy of Estimates Good over entire design space Good over central subset of design space Fair over entire design space; poor for pure quadratic coefficients

Table 1. Comparison of CCD’s.

RSM is to use a set of designed experiments to obtain an optimal response. Box and Wilson used first-degree polynomial model to obtain DOE through RSM and acknowledged that the model is only an approximation and is easy to estimate and apply, even when little information is known about the process. Response Surface Regression method is an assortment of mathematical and statistical techniques useful for modeling and analyzing experiments in which a response variable is influenced by several independent variables. It explores the relationships between several independent variables and one or more response variables; the response variable can be graphically viewed as a function of the process variables (or independent variables) and this graphical perspective of the problem has led to the term Response Surface Method [5]. RSM is applied to fit the acquired model to the desired model when random factors are present and it may fit linear or quadratic models to describe the response in terms of the independent variables and then search for the optimal settings for the independent variables by performing an optimization step. According to Clurkin and Rosen [6], the RSM was constructed to check the model part accuracy which uses the build time as function of the process variables and other parameters. According to Asiabanpour et al. [7], developed the regression model that describes the relationship between the factors and the composite desirability. RSM also improves the analyst’s understanding of the sensitivity between independent and dependent variables [8]. With RSM, the relationship

between the independent variables and the responses can be quantified [9]. RSM is an experimental strategy and have been employed by research and development personnel in the industry, with considerable success in a wide variety of situations to obtain solutions for complicated problems. The following two designs are widely used for fitting a quadratic model in RSM.

1.2.1

Central Composite Designs

Central composite designs (CCDs), also known as BoxWilson designs, are appropriate for calibrating the full quadratic models described in Response Surface Models. There are three types of CCDs, namely, circumscribed, inscribed and faced. The geometry of CCD’s is shown in the Figure 1. Each design consists of a factorial design (the corners of a cube) together with center and star points that allow estimation of second-order effects. For a full quadratic model with n factors, CCDs have enough design points to estimate the .n C 2/.n C 1/=2 coefficients in a full quadratic model with n factors. The type of CCD used (the position of the factorial and star points) is determined by the number of factors and by the desired properties of the design. The following table summarizes some important properties. A design is rotat-

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Review on Application of Response Surface Method to Welding

Figure 2. Box–Behnken design.

able if the prediction variance depends only on the distance of the design point from the center of the design.

1.2.2

nique. One of the main advantages of DOE is that it shows the relationship between parameters and responses. In other words, DOE shows the interaction between variables which in turn allows us to focus on controlling important parameters to obtain the best responses. DOE also can provide us with the most optimal setting of parametric values to find the best possible output characteristics. Besides, the mathematical model generated can be used to predict the possible output response, based on the input values. Another main reason for using DOE is savings on time and cost in terms of experimentation. DOE can determine the number of experiments or the number of runs before the actual experimentation is done. DOE allows to handle experimental errors while still continuing with the analysis. DOE is excellent when it comes to prediction of linear behavior, however, when it comes to nonlinear behavior, DOE does not always give the best results [23]. DOE is extremely helpful in discovering the key variables influencing the quality characteristics of interest in the process. A designed experiment is a test or sequence of tests in which purposeful changes are made to the input variables of a process so that one can observe and identify corresponding changes in the output response.

3

Box-Behnken Designs

Box–Behnken designs (Figure 2) are used to calibrate full quadratic models. These are rotatable and for a small number of factors (four or less), require fewer runs than CCDs. By avoiding the corners of the design space, they allow experimenters to work around extreme factor combinations. Like an inscribed CCD, however, extremes are then poorly estimated. Some extensions of RSM deal with the multiple response problem. Multiple response variables create difficulty, because, what is optimal for one response may not be very optimal for other responses. Other extensions are used to reduce variability in a single response while targeting a specific value, or attaining a near maximum or minimum while preventing variability in that response from getting too large. Significant criticisms of RSM include the fact that the optimization is almost always done with a model for which the coefficients are estimated and not known. That is, an optimum value may only look optimal, but be far from the truth because of variability in the coefficients.

Application of Design of Experiments to Welding

In the present day fabrication industry, welding has become one of the major manufacturing processes frequently used in all types of works. Quality of a weld joint is influenced by welding input parameters that are to be controlled to establish a proper weld. The input parameters selected vary with the type of welding process, thickness and type of base material used. In order to establish the correct combination of input weld parameters trail experiments are to be performed which consumes lot of time and manufacturing cost. Hence statistical techniques are utilised to avoid trial experiments and reduce the manufacturing cost. For that purpose experiments are to be conducted in a sequential manner according to the type of statistical technique selected. Statistical techniques like Factorial Method, Response Surface Method and Taguchi Method are adopted in Design of Experiments to optimize the required output parameters. A thorough review on application of Factorial and Response Surface Method on various welding processes is presented in the following sections. 3.1

Submerged Arc Welding (SAW)

V. Gunaraj et al. [10] adopted RSM for predicting weld bead quality in SAW of pipes. Experiments were conducted based on four-factor, five-level CCD with full replication DOE became a more widely used modeling technique su- technique. Open circuit voltage, wire feed rate, welding perseding its predecessor one-factor-at-time (OFAT) tech- speed and nozzle to plate distance were chosen as input 2

Advantages and Disadvantages of Design of Experiments

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K. Siva Prasad, Ch. Srinivasa Rao and D. Nageswara Rao

parameters and weld penetration, weld width, weld reinforcement and % dilution were chosen as output parameters. Data generated by regression model while developing the Neural Network model trained with Particle Swarm Optimisation.

3.2

Shielded Metal Arc Welding (SMAW)

Saurav Datta et al. [11] evaluated an optimal parameter combination to obtain acceptable quality characteristics of bead geometry in SMAW on mild steel plates. Experiments were conducted using welding current, slag mix percentage and flux basicity index as input process parameters. Adopted 43 (64) full factorial design without replication to obtain bead on plate welds. RSM technique followed by multiple regression method was applied to develop the models.

3.3

Gas Metal Arc Welding (GMAW)

Davi Sampaio Correia et al. [12] compared Genetic Algorithms (GA) and RSM in GMAW welding optimization. The experimental design chosen for the RSM optimization was a CCD composed of a full factorial 23 (three factors, two levels), six axial points and six central points, in a total of 20 runs of experiments. Reference voltage, wire feed rate and welding speed were chosen as input parameters and penetration, deposition, weld width and weld reinforcement were chosen as output parameters. T. Kannan et al. [13] developed mathematical models to predict clad bead geometry and its shape relationships of austenitic stainless steel claddings deposited by GMAW process. The experiments were conducted based on four-factor, five-level CCD with full replication technique. Wire feed rate, welding speed, welding gun angle, nozzle to plate distance were chosen as input parameters and depth of penetration, height of reinforcement and weld bead width were chosen as output parameters. Erdal Karadeniz et al. [14] investigated the effects of various welding parameters on welding penetration in Erdemir 6842 steel having 2.5 mm thickness welded by robotic gas metal arc welding. The welding current, arc voltage and welding speed were chosen as variable parameters. The depths of penetration were measured for each specimen after the welding operations and the effects of these parameters on penetration were researched. J. P. Ganjigatti et al. [15] developed input-output relationships of the MIG welding process using regression analysis based on the data collected as per full-factorial design of experiments. Two levels are considered for each of six input parameters chosen, so that 26 D 64 combinations of input parameters are considered for full factorial DOE. Welding speed, Arc voltage, wire feed rate, gas flow rate, nozzle to plate distance, torch angle were chosen as input parameters and Bead height,

Bead width, Bead penetration were chosen as output parameters. D. S. Nagesh et al. [16] adopted 2n1 fractional factorial experimental design technique to determine the main effects as well as 2-factor interaction effects of GMAW process. Welding speed, arc voltage, welding current, gas flow rate, offset distance were chosen as input parameters and penetration, throat thickness and reinforcement height were chosen as output parameters. Manoj Singla et al. [17] applied Factorial design approach for finding the relationship between the various process parameters and weld deposit area of GMAW process. Anderson P. Paiva et al. [18] developed a multi objective optimization technique based on Principal Component Analysis (PCA) and RSM for gas metal arc welding process. The experiments were conducted based on four-factor, five-level CCD. Peak Current, Background Current, Duty Cycle and Wire feed rate were chosen as input variables and weld bead penetration, weld bead height, weld bead width were chosen as output responses. P. Rajendran et al. [19] developed mathematical models to predict angular distortion for a particular set of parameters in GMAW process. Four factors, five level factorial central composite rotatable design has been used to develop mathematical models to correlate angular distortion with multi-pass process variables. Using the mathematical equations trends of direct and indirect effects of the process variables on the angular distortion are presented in the graphical form and analyzed. R. Choteborsky et al. [20] discuused about development of mathematical equations using a four factor central factorial technique to predict the geometry of the weld bead in the deposition of OK Tubrodur 15.43 electrode onto structural steel S235JR. The models developed have been checked for their adequacy and significance by using the F test and the Student’s t test, respectively. 3.4

Gas Tungsten Arc Welding (GTAW)

M. Balasubramanian et al. [21–24] developed mathematical models to predict and optimize impact toughness, hardness, grain size, tensile strength, weld bead geometry of of pulsed current Gas Tungsten Arc Welding of Ti-6Al-4V Titanium Alloy. The experiments were conducted based on four-factor, five-level CCD with full replication technique. Peak current, base current, pulse frequency and pulse on time were chosen as input parameters for all the predicated outputs. P. K. Giridharan et al. [25] studied Optimization of pulsed GTA welding process parameters for the welding of AISI 304L stainless steel sheets. A CCD with three facto, five level full factorial experimental design consisting of 20 runs was used. A quasi-Newton numerical optimization technique was used to solve the optimization problem. Sudhakaran R. et al. [26] studied optimization of process parameters using genetic algorithm (GA) to optimize depth to width ratio in 202 grade stainless steel gas tungsten arc welded (GTAW) plates. Experiments were conducted

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Review on Application of Response Surface Method to Welding

based on central composite rotatable design and mathematical models were developed correlating the important controllable GTAW process parameters like welding current, welding speed, shielding gas flow rate and welding gun angle with weld bead parameters like depth of penetration, bead width and depth to width ratio. Using these models the direct and interaction effects of the process parameters on weld bead geometry were studied. Optimization of process parameters was done using GA. A source code was developed using Turbo C to do the optimization for depth to width ratio with penetration and bead width as constraints. The optimal process parameters gave a value of 0.9 for depth to width ratio which demonstrates the accuracy and effectiveness of the model presented and program developed. The obtained results help in selecting quickly the process parameters to achieve the desired quality. 3.5

Plasma Transferred Arc Welding (PTAW)

Marimuthtu K. & Murugan N. [27] used five factor, five level factorial technique to predict the geometry of the weld in the deposition of Stellite 6 (Co-Cr-A) alloy onto carbon steel valve seat rings using PTAW process. They reported that optimizing the process parameters reduced the amount of metal deposited and enhanced the mechanical and metallurgical properties of the hardfaced layers. K. Siva et al. [28] adopted central composite rotatable full factorial design matrix and conducted experiments for optimization of weld bead geometry in Plasma transferred arc welding Genetic Algorithm. The experiments were conducted based on five factors, five level CCD matrix to optimize the experimental conditions. A. K. Lakshminarayan et al. [29] predicted the Dilution of Plasma Transferred Arc Hardfacing of Stellite on Carbon Steel using Response Surface Methodology. CCD of second order was employed to establish the mathematical relationship of the response surface using the smallest possible number of experiments without loss of accuracy. The experiments were conducted based on five factors, five level CCD matrix to optimize the experimental conditions. V. Balasubramanian et al. [30] used RSM to predict and optimize the percentage of dilution of iron-based hardfaced surface produced by the PTA (Plasma Transferred Arc Welding) process. The experiments were conducted based on five-factor five-level CCD with full replication technique and a mathematical model was developed using RSM. Furthermore, the RSM was also used to optimize the process parameters that yielded the lowest percentage of dilution. Ramachandran et al. [31] studied the effects of different experimental conditions on the dry sliding wear behavior of stainless steel surface produced by PTA hardfacing process. Mathematical models were developed to estimate wear rate incorporating with rotational speed, applied load and roller hardness using statistical tools such as DOE, regression analysis and analysis of variance. It is found that

the wear resistance of the PTA hardfaced stainless steel surface is better than that of the carbon steel substrate. Siva K. et al. [32] reported the modeling, analysis and optimization of weld bead parameters of nickel based overlay deposited by plasma transferred arc surfacing. The experiments were conducted based on a five factor, five level central composite rotatable design and a mathematical model was developed using multiple regression technique. The direct and interaction effects of input process parameters of PTA Hardfacing on weld bead geometry are discussed. Siva K. et al. [33] developed mathematical equations using multiple regression analysis, correlating various process parameters to weld bead geometry in PTA hardfacing of Colmonoy 5, a nickel-based alloy over stainless steel 316 L plates. The experiments were conducted based on a five factor, five level central composite rotatable design matrix. A genetic algorithm was developed to optimize the process parameters for achieving the desired bead geometry variables. Mohan K. & Muragan N. [34] analyzed the effect of various parameters such as welding current, open circuit voltage, travel speed, nozzle to work distance, shielding gas flow rate and welding position on bead width, height of reinforcement, depth of penetration and percentage of dilution of PTAW tungsten carbide hardfacing of 316 stainless steel plates. The experiments were conducted based on five factor, five level CCD design matrix. Abhishek Jivrag & Shashikant Pople [35] studied the effect of Inconel625 as wear resistant material to control erosion wear. Established the mechanisms of erosion wear on Inconel625, by considering impacting angles of particles at different temperature of Inconel625 substrate as process parameters and wear rate as response parameter. Fractional Factorial Regression method is used for developing relationship between process parameters and response parameter. Siva Prasad K. et al. [36] studied the effect of various process parameters like welding current, torch height and welding speed on front melting width, back melting width and weld reinforcement of PAW welded alloy. The experiments were conducted based on a two level, three factors factorial design. By using the mathematical models the main and interaction effect of various process parameters on weld quality are studied. Zhengyi Jiang et al. [37] used design of experiments based on RSM while developing a robust plasma transfer arc (PTA) coating process. The relative important parameters with respect to surface at hardness values were identified in the Taguchi design. In addition, they applied threedimensional graphs in RSM to develop a robust PTA response surface yielding the desired-better area of a treated layer. Quadratic polynomial with a Box–Behnken design is utilized in their study. The results reveal that RSM provides the effective method as compared to the traditional trialand-error method for exploring the effects of controlled factors on response. Srimanth N. & Murugan N. [38] used five factor, five level factorial technique for developing mathematical equations for the prediction of geometry of the

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K. Siva Prasad, Ch. Srinivasa Rao and D. Nageswara Rao

weld in the deposition of stainless steel SS410L (Cr-Si-Ni) onto carbon seat valve seat rings. The amount of metal deposited has reduced and the mechanical and the metallurgical properties of the hardfaced layers have been enhanced by optimizing the process-parameters. Kondapalli Siva Prasad et al. [39] developed mathematical models to predict weld pool geometry of MPAW welded stainless steel 304L sheets. DOE based on full factorial design is employed for the development of a mathematical model correlating the important controlled pulsed MPAW process parameters like peak current, background current, pulse and pulse width with front width, back width, front height and back height. By using the developed mathematical models effect of pulsed MPAW process parameters on weld pool geometry are studied.

3.6

Plasma Cutting

K. Kadirgama et al. [40] developed mathematical model for prediction of heat affected zone and optimized parameters for air plasma cutting operation on AISI 6061 aluminum alloy. Box–Behnken Design (BBD) was used for optimization of experiments using RSM. Particle Swarm Optimisation (PSO) was employed to optimise cutting parameters. PSO combined with RSM can be very successfully used for reduction of error on time.

3.7

Friction Stir Welding (FSW)

S. Babu et al. [41] developed a mathematical model to predict the tensile strength of friction stir welded AA2219 aluminum alloy. A CCD with four factors and five levels were used to minimize the number of experimental conditions. The RSM was used to develop the model. The developed mathematical model was optimized using the Hooke and Jeeves search technique to maximize the tensile strength of the friction stir welded AA2219 aluminium alloy joints. S. Rajakumar et al. [42] established empirical relationships to predict grain size and tensile strength of friction stir welded AA 6061-T6 aluminum alloy joints. The empirical relationships were developed by RSM incorporating FSW tool and process parameters. A linear regression relationship was also established between grain size and tensile strength of the weld nugget of FSW joints. CCD of second order was used in RSM. R. Palanivel et al. [43] presented a systematic approach to develop the mathematical model for predicting the ultimate tensile strength, yield strength, and percentage of elongation of AA6351 aluminum alloy which is widely used in automotive, aircraft and defense Industries by incorporating (FSW) friction stir welding process parameter such as tool rotational speed, welding speed, and axial force. FSW has been carried out based on three factors five level central composite rotatable design with full replications technique. Response surface methodology (RSM)

is employed to develop the mathematical model. Analysis of variance (ANOVA) Technique is used to check the adequacy of the developed mathematical model. The developed mathematical model can be used effectively at 95% confidence level. The effect of FSW process parameter on mechanical properties of AA6351 aluminum alloy has been analyzed in detail.

3.8

Laser Beam welding (LBW)

K. R. Balasubramaniam et al. [44] investigated Laser welding of Austenitic stainless steel (AISI 304) of thickness 3.0 mm using 2 kW CWNd:YAG laser. The effect of laser power (0.6–1.4 kW), welding speed (0.8–2 m=min) and shielding gas flow rate (5–15 l=min) on the weld-bead geometry i.e. depth of penetration (DOP), weld bead width (BW) were investigated. The experiment was designed on three levels Box-Behnken design with replication. Modeling was done using artificial neural network and multiple regression analysis. The model arrived by using neural network and multiple regression analysis can be utilized for the prediction of process parameters. Ali Khorram et al. [45] investigated laser butt-welding of Ti 6Al 4V using 2.2 kW CO2 laser. RSM is employed to establish the design of experiments and to optimize the bead geometry. The relationships between the input laser-welding parameters (i.e. laser power, welding speed and focal point position) and the process responses (i.e. welded zone width, heat affected zone width, welded zone area, heat affected zone area and penetration depth) are investigated. The multi-response optimizations are used to optimize the welding process. The optimum welding conditions are identified in order to increase the productivity and minimize the total operating cost. The validation results demonstrate that the developed models are accurate with low percentages of error (less than 12.5%).

3.9

Cladding

T. Kannan et al. [46] established a relationship between process parameters and Ferrite number for duplex stainless steel clad metals using RSM. The experiments were conducted based on four-factor, five-level CCD with full replication technique. Welding current, welding speed, contact tip to work piece distance, welding gun angle were chosen as input parameters and Ferrite Number and % dilution were chosen as output parameters. The results indicate that Ferrite Number decreases with the rise in heat input and dilution. Ferrite Number decreases with a rise in welding current and welding speed and increases with a decrease in welding gun angle and rise in contact tip to work piece distance.

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Review on Application of Response Surface Method to Welding

3.10

Electron Beam Welding (EBW)

K. Diana Jennifer et al. [47] used factorial method to predict weld bead geometry in EBW. Two level full factorial method was used to construct the design matrix. Eight experiments were conducted for three factors and two levels. Welding current, welding speed and Vacuum were chosen as input parameters and weld width, weld penetration and weld penetration shape factor were chosen as output parameters.

4

Conclusions

The research work reported so far reveals the following conclusions in establishing DOE. 

“Factorial”, or “Classical DOE”, was the first method used with designed experiments, it allows the user to see which factors are most important and helps to identify important interactions among the factors. It doesn’t predict the best factor levels to meet the desired goals.



Response Surface Methodology (RSM) uses model to make contour plots of predicted behavior. Using these plots, the best combination of factors to meet the desired goals can be predicted.



RSM has an edge over the Taguchi method in terms of significance of interactions and square terms of parameters.



Using RSM, only two control factors may be viewed at a time on a single contour plot although more than about four responses on one graph becomes very difficult to interpret. However, since a response surface is available an automatic optimizer can be used to help in determining the optimum setting for each response.



In most of the works reported, the researchers used four factor, five level, CCD design for conducting the experiments. However very few works are reported on Box Behnken Design because of its limitation on number of factors (mostly suitable for less than four factors).



However, one may use any type of optimization methods such as Artificial Neural Networks (ANN), Genetic Algorithms (GA), Fuzzy, Particle Swarm Optimisation (PSO) etc., after selecting appropriate DOE for any method of welding phenomena.

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[2] Montgomery, D. C., Design and Analysis of Experiments, 3rd Ed.; Wiley: New York, 1991. [3] Wang., C. C., Lin., T. W., Hu, S. S., Optimizing the rapid prototyping process by integrating the taguchi method with the Gray relational analysis. Rapid Prototyping Journal, 13(5), 2007, 304–315. [4] Alagumurthi, N., Palaniradja, K., Soundararajan, V., “Optimization of Grinding Process Through Design of Experiment (DOE)—A Comparative Study”, Materials and Manufacturing Processes, 21: 1, 2006, 19–21. [5] Myers, R., Montgomery, D., Response Surface Methodology. 2nd ed. Wiley: New York, 2002. [6] Mc Clurkin, J. E.,Rosen, D. W., Computer-aided build style decision support for stereo lithography. Rapid Prototyping Journal, 4(1), 2002, 4–9. [7] Asiabanpour. B., Khoshnevis, B., Palmer, K., Development of a rapid prototyping system using response surface methodology, Journal of Quality and Reliability Engineering International, 22(8), 2006, 919–937. [8] Bauer., W. K., Parnell, S. G., Meyers, A. D., Response Surface Methodology as a Sensitivity Analysis Tool in Decision Analysis. Journal of Multi-Criteria decision Analysis, 8, 1999, 162–168. [9] Kechagias, J., An experiment investigation of the surface roughness of parts produced by LOM process. Rapid Prototyping Journal, 13(1), 2007, 17–22. [10] V. Gunaraj, N. Murugan, Application of response surface methodology for predicting weld bead quality in SMAW of pipes, Journal of Materials Processing Technology 88, 1999, 266–275. [11] S. Datta, A. Bandyopadhyay, P. K. Pal, Modeling and optimization of features of bead geometry including percentage dilution in submerged arc welding using mixture of fresh flux and fused slag, Int J Adv Manuf Technol 36, 2008, 1080– 1090. [12] D. S. Correia, C. V. Goncalves, Sebastiao S. C. Junior, V. A. Ferraresi, Comparison between genetic algorithms and response surface methodology in GMAWwelding optimization, Journal of Materials Processing Technology, 160, 2005, 70–76. [13] T. Kannan, N. Murugan, Prediction of Ferrite Number of Duplex stainless steel clad Metals using RSM, welding journal, BHEL, 2006, 91–100. [14] E. Karadeniz, U. Ozsarac, C. Yildiz, The effect of process parameters on penetration in gas metal arc welding processes, Materials and Design 28, 2005, 649–656. [15] J. P. Ganjigatti, D. K. Pratihar, A. Roy Choudhury, Modeling of the MIG welding process using statistical approaches, Int J Adv Manuf Technol 35, 2008, 1166–1190. [16] D. S. Nagesh, G. L. Datta, Modeling of fillet welded joint of GMAW process: integrated approach using DOE, ANN and GA, Int J Interact Des Manuf 2, 2008, 127–136. [17] M. Singla, D. Singh, D. Deepak, Parametric Optimization of Gas Metal Arc Welding Processes by Using Factorial Design Approach, Journal of Minerals & Materials Characterization & Engineering, 9(4), 2010 pp. 353–363. [18] A. P. Paiva, S. C. Costa, E. J. Paiva, P. P. Balestrassi, J. R. Ferreira, Multi-objective optimization of pulsed gas metal arc welding process based on weighted principal component scores, Int J Adv Manuf Technol, 50, 2010, 113–125. [19] P. Rajendran, V. R. Sivakumar, V. Gunaraj, V. Vel Murugan, Statistical analysis on angular distortion of welded structural steel plates, International Journal of Engineering Science and Technology, 3(4), 2011, 3404–3421.

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